SOLUTION: 6. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 6. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.       Log On


   

Question 187210: 6. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.

z^2 + z + 1 = 0
help please. thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

From z%5E2%2Bz%2B1 we can see that a=1, b=1, and c=1


D=b%5E2-4ac Start with the discriminant formula.


D=%281%29%5E2-4%281%29%281%29 Plug in a=1, b=1, and c=1


D=1-4%281%29%281%29 Square 1 to get 1


D=1-4 Multiply 4%281%29%281%29 to get %284%29%281%29=4


D=-3 Subtract 4 from 1 to get -3


Since the discriminant is less than zero, this means that there are two complex solutions.


In other words, there are no real solutions.